In some current telecommunications systems, the use of costant-amplitude modulations, for example phase or frequency modulations, is preferred, because the latter make it possible to maximize the range of said systems. In practice, the transmission power is constant and at maximum in this case.
In the case of a continuous-phase modulation, there are two known advantages:                A reasonable spectral occupancy, which results in reduced interference between adjacent transmission channels,        A constant amplitude which makes it possible to use the output amplifiers of the transmitters at the maximum of their power, without having to worry too much about their amplitude linearity. This makes it possible to optimize the link budget, with a given average transmission power.        
Among these modulations, one of the most widely used, particularly in mobile radio telephony, is GMSK modulation. The latter has been adopted because of its frequency spectrum which exhibits a maximum decrease as a function of the deviation relative to the carrier frequency. It is a binary (and therefore two-state) modulation, and of differential type in that, when two successive bits to be transmitted are different (0/1 or 1/0), the carrier undergoes a total phase rotation of +π/2 or of −π/2 otherwise.
The CPM modulations are in practice completely defined by a frequency pulse and by the modulation index h such that the average of the absolute value of the phase rotation is h π. Most of the time, and for the purposes of simplicity of implementation of the receiver, h is ½.
However, the duration of the frequency pulse associated with a given bit is not limited to the duration of a bit. Thus, for the GMSK modulation mentioned previously, it ought to be infinite since, by definition, the Gaussian curve is of infinite length. In practice, a limit of finite duration (2 or 3 bits) is imposed, such that the performance degradation compared to the theoretical case is negligible.
As long as the system is limited to the binary case, the receiver remains relatively simple.
A theory expounded in the mid 1980s, explained in the publication “Exact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses (AMP)”, Pierre. A. Laurent, IEEE Transactions on Communications, Vol. COM-34, No 2, February 1986, pp 150-160, showed that this type of modulation could be approximated by a conventional amplitude and phase modulation and therefore be demodulated by a receiver of low complexity. This is true only in the binary case (1 bit per symbol).
At the current time, the needs in terms of useful bit rate have greatly increased, so much so that there is a desire to generalize the CPM modulations to more than two states: four states make it possible to convey not one bit per symbol but two, eight states 3 bits and 16 states 4 bits.
Unfortunately, even in the case with 4 states, the receiver becomes much more complex than in the case with two states because the inter-symbol interference inherent in this kind of modulation considerably complicates the problem: the signal received for a given symbol depends on its state and on those of its neighbors and the number of configurations becomes so great that there is no simple way to decide on the value of said symbol.
Moreover, the increase in bit rate also entails increasing the modulation speed with the attendant problem of the appearance of problems due to propagation: it may be that, at a given instant, the signal is received in direct sight of the transmitter, but with one or more delayed replicas (reflections on buildings, etc.) that have delays that are not inconsiderable in relation to the duration of a symbol, or even significantly greater. This further increases the complexity of the receiver.
To the knowledge of the Applicant, in the case of a constant or quasi-costant-amplitude modulation, there is no transmission-reception system, of simple design, when the number of states envisaged is greater than 2.